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Evaluate : int(-1)^(3/(2))|x"sin"(pix)|d...

Evaluate : `int_(-1)^(3/(2))|x"sin"(pix)|dx`

Text Solution

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`abs(xsin(pix))={xsinpix,x in (-1,1); -x sinpix,x in (1,3/2)`
`int_1^(3/2) abs(xsin(pix))dx=int_-1^1 xsin(pix)dx +int_1^(3/2) -xsin(pix)dx`
`abs{(-xcospix)/pi}_-1^1-int_-1^1{(-cospixdx)/pi}-{abs(-xcos(pix))/pi}_1^(3/2)-int_1^(3/2) (-cosx dx)/pi`
`=1/pi-(-1/pi)+0-{-1/pi-(1/(pi^2))}`
`=1/pi+1/pi+1/pi+1/pi^2`
`=3/pi+1/pi^2`
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